The Markov property for classes of nonlinear parabolic equations

A nonlinear strongly continuous contraction semigroup, on a Hilbert space L -2(X, m) is said to satisfy the Markov property if it is order preserving a nd contractive on L-infinity(X,m). We prove that such property holds for cl asses of nonlinear parabolic evolution equations including those governed b y suitable nonlinear second order differential operators in divergence form with measurable coefficients, whose basic example is the p-laplacian opera tor, and the infinite dimensional p-Ornstein-Uhlenbeck operator on abstract Wiener spaces.